This is the peer reviewed version of the following article: [Nguyen, V. P., Lloberas-Valls, O., Stroeven, M. and Sluys, L. J. (2012), Computational homogenization for multiscale crack modeling. Implementational and computational aspects. Int. J. Numer. Meth. Engng, 89: 192–226. doi:10.1002/nme.3237], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.3237/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving

A computational homogenization procedure for cohesive and adhesive crack modeling of materials with a heterogeneous microstructure has been recently presented in Computer Methods in Applied Mechanics and Engineering (2010, DOI:10.1016/j.cma.2010.10.013). The macroscopic material properties of the cohesive cracks are obtained from the inelastic deformation manifested in a localization band (modeled with a continuum damage theory) at the microscopic scale. The macroscopic behavior of the adhesive crack is derived from the response of a microscale sample representing the microstructure inside the adhesive crack. In this manuscript, we extend the theory presented in Computer Methods in Applied Mechanics and Engineering (2010, DOI:10.1016/j.cma.2010.10.013) with implementation details, solutions for cyclic loading, crack propagation, numerical analysis of the convergence characteristics of the multiscale method, and treatment of macroscopic snapback in a multiscale simulation. Numerical examples including crack growth simulations with extended finite elements are given to demonstrate the performance of the method

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